Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 11, Problem 8P
The v = 0 to v = 1 vibrational transition of the HI molecule occurs at a frequency of 6.69 × 1013 Hz. The same transition for the NO molecule occurs at a frequency of 5.63 × 1013 Hz. Calculate (a) the effective force constant and (b) the amplitude of vibration for each molecule. (c) Explain why the force constant of the NO molecule is so much larger than that of the HI molecule.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The effective spring constant describing the potential energy of the HBr molecule is 410 N/m and that for the NO molecule is 1530 N/m.
(a) Calculate the minimum amplitude of vibration for the HBr molecule.
(b) Calculate the minimum amplitude of vibration for the NO molecule.
The frequency of the photon that causes the υ = 0 to υ = 1 transition in the CO molecule is 6.42 x 1013 Hz. We ignore any changes in the rotational energy for this example.(A) Calculate the force constant k for this molecule. (B) What is the classical amplitude A of vibration for this molecule in the υ = 0 vibrational state?
The potential energy of two atoms in a diatomic molecule is approximated by U(r) = a/r12-b/r6, where r is the spacing between atoms and a and b are positive constants.
Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it -
that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. Express your answer in terms of the variables a and b.
For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13\times 10-10m and the dissociation energy is 1.54\times 10-18J per
molecule. Find the value of the constant a. Express your answer in joules times meter in the twelth power. Find the value of the constant b. Express your answer in joules
times meter in the sixth power.
Chapter 11 Solutions
Modern Physics
Ch. 11.2 - Compare the effective force constant for the CO...Ch. 11 - Prob. 1QCh. 11 - Prob. 2QCh. 11 - Prob. 3QCh. 11 - Prob. 4QCh. 11 - Prob. 5QCh. 11 - Prob. 7QCh. 11 - Prob. 8QCh. 11 - Prob. 9QCh. 11 - Prob. 1P
Ch. 11 - Use the data in Table 11.2 to calculate the...Ch. 11 - The CO molecule undergoes a rotational transition...Ch. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - The v = 0 to v = 1 vibrational transition of the...Ch. 11 - Consider the HCl molecule, which consists of a...Ch. 11 - Prob. 10PCh. 11 - Prob. 11PCh. 11 - Prob. 12PCh. 11 - Prob. 13PCh. 11 - Prob. 14PCh. 11 - Prob. 15PCh. 11 - Prob. 18P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.arrow_forwardA gas of identical diatomic molecules absorbs electromagnetic radiation over a wide range of frequencies. Molecule 1, initially in the υ = 0 vibrational state, makes a transition to the υ = 1 state. Molecule 2, initially in the υ = 2 state, makes a transition to the υ = 3 state. What is the ratio of the frequency of the photon that excited molecule 2 to that of the photon that excited molecule 1? (a) 1 (b) 2 (c) 3 (d) 4 (e) impossible to determinearrow_forwardA molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (i) every collision is effective in deactivating the molecule rotationally and (ii) that one collision in 10 is effective. Calculate the width (in hertz) of rotational transitions in the molecule.arrow_forward
- A rigid tank of volume V = 0.02 m3 contains carbon monoxide at a temperature of T0 = 25° C and a pressure of P0 = 9.00 × 105 Pa. This molecule should be treated as a diatomic ideal gas with active vibrational modes. a)The temperature of the gas increases by 10° C. Calculate the pressure of the gas in pascal at this increased temperature. b)Calculate the change to the internal energy of the gas in joules. c)Calculate the change in the entropy of the gas in joules per kelvin.arrow_forwardQ3: The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = - 읆 옮 , where a and b are constant and x is the distance between the atoms. If the dissociation energy of the molecule is (U(x= ∞) -U at equilibrium), D is (a) b²/6a (b) b²/2a (c) b²/12a (d) b²/4aarrow_forwardThe air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal gas at temperature 100 °C, what is the average kinetic energy for each of the molecule in air?(Consider Oxygen, Nitrogen, and carbon dioxide as diatomic molecule structure which consist of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kB = 1. 38 x 10 23 J/Karrow_forward
- Homework 6 Problem 6: A rigid tank of volume V = 0.015 m3 contains carbon monoxide at a temperature of T0 = 21° C and a pressure of P0 = 9.00 × 105 Pa. This molecule should be treated as a diatomic ideal gas with active vibrational modes. Part (a) Calculate the pressure of the gas in pascal at this increased temperature. P = ______ Part (b) Calculate the change to the internal energy of the gas in joules. ΔU = ______ Part (c) Calculate the change in the entropy of the gas in joules per kelvin. ΔS = ______arrow_forwardA molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally and (b) that one collision in 10 is effective. Calculate the width (in cm-1) of rotational transitions in the molecule.arrow_forwardThe force constant of the Cl2 molecule is 323 Nm-1. Calculate the energy at the zero point of vibration and if this amount of energy is converted to translational energy, how fast would the molecule be moving?arrow_forward
- A rigid tank of volume V = 0.014 m3 contains carbon monoxide at a temperature of T0 = 25° C and a pressure of P0 = 9.00 × 105 Pa. This molecule should be treated as a diatomic ideal gas with active vibrational modes. Part (a) In this model, how many degrees of freedom does each molecule of carbon monoxide have? Part (b) The temperature of the gas increases by 10° C. Select the process that has occurred from the choices below. Part (c) Calculate the pressure of the gas in pascal at this increased temperature. Part (d) Calculate the change to the internal energy of the gas in joules. Part (e) Calculate the change in the entropy of the gas in joules per kelvin. I know you cannot answer all parts however manyuo can will helparrow_forwardMolecular Pair Potential The vibrational properties of a diatomic molecule can often be described by Mie's pair potential 3: U(r) = C c[9₁-9] (4) where U(r) is the potential energy between the two atoms, r is the distance between the two atoms, C, o are positive constants, and λ > 6 is a constant. The case with X 12 is the Lennard-Jones potential and was covered in Lecture #2. For the purposes of this problem, assume there is a mass ‘m’ that represents the dynamical mass of the molecule. 4 TLTR: (a) Find a combination of C, m, o that has the units of frequency. (b) Derive the ratio of the equilibrium positions and of the frequencies of small oscillations for X 10, 14. Show that the units for the equilibrium position and for the frequency of the oscillations are consistent.arrow_forwardThe air is a gas mixture of oxygen, carbon dioxide, and Nitrogen. If the air can be treated as ideal gas at temperature 100 °C, what is the average kinetic energy for each of the molecule in air?(Consider Oxygen, Nitrogen, and carbon dioxide as diatomic molecule structure which consist of translational and rotational degree of freedom only. No vibration motion is considered) Boltzmann constant is kg 1. 38 x 10-231/Karrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY